I have a client that when she does push ups or tricept dips she says she has pain in her coller bone. What could cause this?

Best to check with a doctor if its really pain.

First and foremost, stop doing that exercise, or as Bethany alluded to, stop doing any exercise that causes pain. Second, in my opinion, there is little real life use for the tricep dip exercise anyway, and it puts the should joint in a compromised terminal position, against significant force. Finally, telling your client to see a doctor, though sensible, may not be the issue as he/she may have already seen one, or have another extenuating circumstance. Only you and this person can best discuss this option. But, I would certainly bring that up.

If your client has pain doing dips, it means that they either lack the strength for this exercise, or have a tendon or joint problem. Which to you should indicate that less extreme movements, and/or resistance should be part of your clients workout. Generally stated, do safer movements, against less force, and maybe smaller ranges of movement. Make sure that whatever you do with this client, that there is ZERO joint pain during the movement(s). Many trainers tend to rush a clients progress by adding weight, and more advance movements sooner than they should, in order to speed up a clients results. But remember, they are not you, and things take time.

As everyone state above, have them get checked out by a doctor, preferably by a shoulder specialist. Usually when there is pain during those movements in the collar bone (aka - clavical) it'll stem from the shoulder joint(s).

The shoulder is a complex region because of the numerous interdependent joints, which are: glenohumeral (GH), sternoclavicular, acromioclavicular, and scapulothoracic joints. Note that 2 of the 4 joints listed have "clavicular" in the name which are joints that deal directly with the clavical or collar bone.

As already mentioned above, it is best that she go see her doctor. It's particularly difficult to answer without having done a movement screen. However, pain is a good indicator to go see the doctor.

Any pain that occurs during exercise should be thoroughly assessed by a professional: medical and/or sports doctor, physiotherapist, chiropractor, etc..

The pain could be many things, as mentioned above; I've seen lots of wrist, elbow, shoulder weaknesses creep up the kinetic chain. Also, the position of the shoulder during both exercises has to be strong and stable, or pain will likely result. Does she do anything outside of her training with you that might cause similar strain?

Certainly there countless other things she can do to train the same muscles, so best to go there until a formal diagnosis has been made. Then, you and she can talk and form a new plan.

Best wishes!
Michelle

Of course see a specialist.
However is it just these exercises the dip, and pushups? Have you tried alternate exercises or modified exercises. If so does she have pain when modified or alternate exercises used. She may simply not be ready for these body weight exercises.
I would have her see a doctor and try modified and alternate exercises targeting these areas. ( also I never much liked the dip , I feel it places too much pressure on the joints).